Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x-6y &= -9 \\ -x+4y &= 8\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = -4y+8$ Divide both sides by $-1$ to isolate $x$ $x = {4y - 8}$ Substitute this expression for $x$ in the first equation. $3({4y - 8}) - 6y = -9$ $12y - 24 - 6y = -9$ Simplify by combining terms, then solve for $y$ $6y - 24 = -9$ $6y = 15$ $y = \dfrac{5}{2}$ Substitute $\dfrac{5}{2}$ for $y$ in the top equation. $3x-6( \dfrac{5}{2}) = -9$ $3x-15 = -9$ $3x = 6$ $x = 2$ The solution is $\enspace x = 2, \enspace y = \dfrac{5}{2}$.